I just started inseming with fresh KD sperm. I bought my shipping kit from babydustdelivery. So far, so good. The cost is great; they sell a kit with 5 vials of test yolk buffer (TYB) for $100 (plus $35 S/H to send it to your donor), so you can reuse the shipper and ice pack from month to month. The one vial kit is $60 and S/H is still $35, so buying the bulk kit makes a lot of sense, financially.
We're shipping from Chicago to VT and it costs $68 for overnight shipping (Fedex and UPS are about the same), $90-ish for a Saturday delivery (haven't had to do this yet). Then, if I know I'm going to need a new shipment the next month, I just send it back to KD by regular mail (about $6).
The "production"/shipping process is pretty straightforward (and the kit comes with instructions about warming the TYB before mixing the semen in and such).
The biggest hassle for me so far has been working around weekends. When you get a positive OPK, you want an overnight shipment to go out that day, to catch your O the following day. So, if you get a positive OPK on Saturday or Sunday, the timing won't work. My first try, in February, I ended up inseming on what was probably O+1, with 2-day old sperm (they're supposed to make it about 24 hrs in the TYB) because of the weekend and some communication issues with my KD. So, obviously you can only control what you can control, but it's definitely worth thinking about when the weekend(s) will fall in your wife's likely O window. For me, I O 95% of the time between CD14 and CD 20, so if I haven't had a positive OPK by CD18 and it's a Friday, I'm going to go ahead and ask KD to ship, because it's really likely that I'll O on Sunday, and I'd rather insem early than late.
Anyway, I'm still fairly new at this whole process, and there are people on this board who've gotten pregnant doing fresh shipped sperm, who may be able to give you more seasoned advice, but just wanted to share my little bit of (l)earned wisdom.
And, definitely, come join us in the Queer Conceptions thread! There's a huge diversity of different experiences being shared, and it's a great place to get support as you go through the ups and downs of TTC. (Fingers crossed, of course, for more ups than downs, and a speedy departure to the Queer Pregnant and Parenting Thread.)